Highest Common Factor of 67, 512, 119, 362 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 67, 512, 119, 362 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 67, 512, 119, 362 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 67, 512, 119, 362 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 67, 512, 119, 362 is 1.
HCF(67, 512, 119, 362) = 1
HCF of 67, 512, 119, 362 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 67, 512, 119, 362 is 1.
Highest Common Factor of 67,512,119,362 is 1
Step 1: Since 512 > 67, we apply the division lemma to 512 and 67, to get
512 = 67 x 7 + 43
Step 2: Since the reminder 67 ≠ 0, we apply division lemma to 43 and 67, to get
67 = 43 x 1 + 24
Step 3: We consider the new divisor 43 and the new remainder 24, and apply the division lemma to get
43 = 24 x 1 + 19
We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get
24 = 19 x 1 + 5
We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get
19 = 5 x 3 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 67 and 512 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(43,24) = HCF(67,43) = HCF(512,67) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 119 > 1, we apply the division lemma to 119 and 1, to get
119 = 1 x 119 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 119 is 1
Notice that 1 = HCF(119,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 362 > 1, we apply the division lemma to 362 and 1, to get
362 = 1 x 362 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 362 is 1
Notice that 1 = HCF(362,1) .
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Frequently Asked Questions on HCF of 67, 512, 119, 362 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 67, 512, 119, 362?
Answer: HCF of 67, 512, 119, 362 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 67, 512, 119, 362 using Euclid's Algorithm?
Answer: For arbitrary numbers 67, 512, 119, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.